Solution to Laplace's equation in spherical co-ordinates

[jdmo]

I have a question about the general solution to Laplace's equation in spherical co-ordinates, which takes the form of a linear combination of the spherical harmonics. In my problem, I am solving for the potential within two concentric spherical shells, each with its own conductivity. Now, since the outer volume does not contain the origin, am I right to assume that the coefficients B_{lm} do not vanish? For the inner volume, which does contain the origin, am I right in assuming that the coefficients B_{lm} do vanish?

 

[Meir Achuz]

Yes. In between the spheres, neither A nor B vanishes.